Question

If Susie is late for school one particular day of the week, the probability she arrives on time the next day is 0.8. If she arrives on time one day, the probability she arrives late the following day is 0.3. Susie was on time on Monday. What is the probability she was late on Thursday

Answer 1

0.273 = 27.3% probability that she was late on Thursday.

Explanation:

On time on Monday, late on Thursday:

Possible outcomes (tuesday-wednesday-thursday).

on time(0.7 probability) - on time(0.7 probability) - late(0.3 probability)

on time(0.7 probability) - late(0.3 probability) - late(0.2 probability)

late(0.3 probability) - on time(0.8 probability) - late(0.3 probability)

late(0.3 probability) - late(0.2 probability) - late(0.2 probability).

What is the probability she was late on Thursday?

Sum of these four outcomes. So

`p = 0.7*0.7*0.3 + 0.7*0.3*0.2 + 0.3*0.8*0.3+0.3*0.2*0.2 = 0.273`

0.273 = 27.3% probability that she was late on Thursday.